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Test corpuscles in general relativity

Published online by Cambridge University Press:  20 January 2009

H. P. Robertson
H. P. Robertson
Affiliation:
Princeton University
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In the general theory of relativity, as in many other branches of theoretical physics, the material and energetical content of spacetime is considered, in the first instance, as an extended field, which is specified by means of field quantities (energy-momentum-stress tensor, charge-current density, electromagnetic field strength). From this point of view corpuscles (material particles, photons) are constructs obtained by first considering the field quantities as nonvanishing only within certain world tubes, and then passing by limiting processes to the idealisation in which these world tubes are shrunk into world lines. More precisely, this passage to the corpuscular description may be thought of as accomplished by replacing the original field by successive members of a sequence of field distributions, satisfying the same field laws, which cluster more and more in the neighbourhood of the world lines, and for which in some significant sense the total measure approaches a finite limit. Each such world line, together with the limiting measures of those portions of the field quantities associated therewith, is then a corpuscle; the form of the world line determines the motion of the corpuscle, and the associated “corpuscular quantities” its physical attributes (mass or energy, momentum, charge).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 5 , Issue 2 , June 1937 , pp. 63 - 81
Copyright
Copyright © Edinburgh Mathematical Society 1937

References

page 72 note 1 Above all, by Weyl, H. in his important treatise Raum-Zeit-Materie;Google Scholar we shall here refer to the 5th edition of this work, although many of the results are to be found in the earlier editions. They are also obtained, although from a less fundamental standpoint, in the standard English work, Eddington, A.S., The Mathematical Theory of Relativity (Cambridge, 1923).Google Scholar

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page 76 note 1 The necessity of demanding that the limiting “mass-centre” of the field fall no the path L, which is here insured by our formulation of (d), has been pointed out by A. Einstein and W. Mayer in a discussion with the writer.

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page 77 note 1 Cf. the work of Halpern, O., Phys. Rev. 48, p. 431 (1935),CrossRefGoogle Scholar where it is shown that, on the classical theory, a plane wave field, whose energy-momentum-stress tensor is symmetrical and satisfies the condition (6.1), is necessarily propagated with the velocity of light.

page 76 note 2 Proc. Boy. Soc. Edin. 53, p. 43 (1932).Google ScholarCf. also Synge, J. L., Quart. Journ. Math. (Oxford) 6, p. 199 (1935),Google Scholar who shows that their assumption of the parallel transport of si can be replaced by energy-momentum considerations concerning the interaction of the material source and receiver in establishing the possibility of a photon description in general relativity; the justification of these assumptions, from the present standpoint, is considered in the succeeding § 7.

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